Theorems · Theorem · group theory
Multiset.sum_cons
∀ {M : Type u_3} [inst : AddCommMonoid M] (a : M) (s : Multiset M), (a ::ₘ s).sum = a + s.sum- Cited by
- 45 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- Multisetstatement and proof · cited by 2,627
- Multiset.sumstatement · cited by 388
- Multiset.consstatement · cited by 313
- Multiset.foldr_consproof · cited by 4
Cited by45
Results whose statement or proof uses this declaration.
- Multiset.sum_singletonproof · cited by 26
- Multiset.join_consproof · cited by 9
- Equiv.Perm.sign_of_cycleTypeproof · cited by 7
- Multiset.sum_map_mul_rightproof · cited by 5
- Multiset.le_sum_of_memproof · cited by 5
- Multiset.dvd_sumproof · cited by 4
- ADEInequality.sumInv_pqrproof · cited by 4
- Polynomial.Monic.nextCoeff_multiset_prodproof · cited by 3
- Polynomial.derivative_prodproof · cited by 3
- Polynomial.natDegree_multiset_prod'proof · cited by 3
- Multiset.sum_map_mul_leftproof · cited by 3
- card_support_eq_three_iffproof · cited by 3